why just cheap Chinese products? Any cheap product is probably that way because it has been made by cheap labour somewhere. The British seem to me particularly eager to buy things cheap and boast how little they paid, whether it's shoes or holidays. That's why the Chinese get away with it: we don't just let them, we actively encourage it.
But making things cheaply to sell abroad has actually been the salvation of some countries - remember when Japan was chiefly known for low-cost goods? Or when everything seemed to be made in Korea? The money these countries made has turned them into wealthy nations; as people there get rich, their labour is no longer cheap and the business of sewing T-shirts goes elsewhere. So you have to consider whether a boycott would simply keep China impoverished, and whether this is a good thing.